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Find the approximate area under the curve y= sqrt{x^2+1} on the interval [0,1] using the trapezoid method and 5 subintervals.
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.

y' = x^2 + y^2, y(0) = 3; y(0.5)

y(0.5) ≈ _______ (h = 0.1)
y(0.5) ≈ _______ (h = 0.05)
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.

y' = x2 + y2, y(0) = 3; y(0.5)

y(0.5) ≈ _________ (h = 0.1)
y(0.5) ≈ _________(h = 0.05)
Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05.

y' = x2 + y2, y(0) = 3; y(0.5)

y(0.5)≈ ________ (h = 0.1)
y(0.5)≈ ________ (h = 0.05)
The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 6 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds? Assume that the confidence level is to be 99%.
Using Bessel’s difference interpolation formula, to compute the value of y(5) for the
following data given below:
x: 0 4 8 12
y: 14.27 15.81 17.72 19.96
solve for t in the following equation by means of linear interpolation
( 1+ t )^10 - 1/ t = 25

Approximate the solution to the following partial differential equation using the Backward-Difference method. ∂u /∂t − ∂2u/ ∂x2 =0, 0 < x < 2, 0 < t; u(0,t) =u(2,t) =0, 0 < t, u(x,0) =sin( π /2) x,0 ≤x ≤2. Use m = 4, T = 0.1, and N = 2, and compare your results to the actual solution u(x,t) = e−((π2/4)t)* sin( π)

Solve this without MATLAB and need Step by step

From the following data find f'(5).
x= 1 3 4 6
F(x)= 14 2 8 9
Using the Horner’s method find the values of f(4) and f'(4) for the polynomial
f(x) = x^4 +2x^3 −x^2 +1.
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